Publicado

2017-01-01

Fuzzy sets. A way to represent ambiguity and subjetivity

Conjuntos difusos. Una forma de representar la imprecisión y la subjetividad

Palabras clave:

fuzzy sets theory, linguistic variable, fuzzy numbers (en)
teoría de los conjuntos difusos, variable lingüística, números difusos (es)

Descargas

Autores/as

  • José Rubén Niño Quevedo Universidad Nacional de Colombia
Mathemathical modeling seeks to describe in a formal way a phenomenom but we can encounter two inconveniences, namely, the complexity and the uncertainty by vagueness. In order to take vagueness into consideration, the fuzzy set theory formalized by Zadeh in 1965 intends to give a mathematical treatment to the subjective topics. Additionally, it is considered as an important tool for getting a better understanding of some real situations. This is why we are motivated to give in this paper some of the basics notions of this branch of mathematics which has been in a continuous development for the latest fifty years.
La modelación matemática busca describir de manera formal un fenómeno pero podemos encontrar dos inconvenientes, a saber, la complejidad y la incertidumbre por "ambigüedad". Para considerar la ambigüedad, la teoría de los conjuntos difusos formalizada por Zadeh en 1965 pretende dar un tratamiento matemático a los temas subjetivos. Adicionalmente, se le considera una herramienta importante para obtener un mejor entendimiento de algunas situaciones reales. Éste en el por qué se motivó a presentar, en este escrito, algunas de las nociones básicas de esta rama de las matemáticas que ha estado en continuo desarrollo durante los últimos cincuenta años.

Referencias

B. Bede, Studies in fuzziness and soft computing 295 - Mathematics of Fuzzy Sets and Fuzzy Logic, Springer, 2013.

J. J. Buckley and E. Eslami, An introduction to fuzzy logic and fuzzy sets, vol. 13, Springer Science & Business Media, 2002.

A. Celikyilmaz and I. B. Turksen, Modeling uncertainty with fuzzy logic, Studies in Fuzziness and Soft Computing 240 (2009).

R. Coppi, M. A. Gil, and H. A. Kiers, The fuzzy approach to statistical analysis, Computational statistics & data analysis 51 (2006), no. 1, 1–14.

E. Cox, M. O’Hagan, R. Taber, and M. O’Hagen, The fuzzy systems handkbook with cdrom, Academic Press, Inc., 1998.

P. Diamond and P. Kloeden, Metric topology of fuzzy numbers and fuzzy analysis, Fundamentals of Fuzzy Sets, Springer, 2000, pp. 583–641.

P. Diamond, P. E. Kloeden, P. E. Kloeden, Australia Mathematician, and P. E. Kloeden, Metric spaces of fuzzy sets: theory and applications, World Scientific, 1994.

V. Dimitrov and V. Korotkich, Fuzzy logic: a framework for the new millennium, vol. 81, Springer Science & Business Media, 2002.

D. Dubois, H. M. Prade, and H. Prade, Fundamentals of fuzzy sets, vol. 7, Springer Science & Business Media, 2000.

D. J. Dubois, Fuzzy sets and systems: Theory and applications, vol. 144, Academic press, 1980.

B. A. Faybishenko, Introduction to modeling of hydrogeologic systems using fuzzy differential equations, Fuzzy Partial Differential Equations and Relational Equations, Springer, 2004, pp. 267–284.

M. A. Gil, M. L´opez-D´ıaz, and D. A. Ralescu, Overview on the development of fuzzy random variables, Fuzzy sets and systems 157 (2006), no. 19, 2546–2557.

M. Hanss, Applied fuzzy arithmetic, Springer, 2005.

L. C. Jain and N. M. Martin, Fusion of neural networks, fuzzy systems and genetic algorithms: Industrial applications, vol. 4, CRC press, 1998.

V. Lakshmikantham and R. N. Mohapatra, Theory of fuzzy differential equations and inclusions, CRC Press, 2004.

K. H. Lee, First course on fuzzy theory and applications, vol. 27, Springer Science & Business Media, 2006.

J. N. Mordeson, D. S. Malik, and T. D. Clark, Application of fuzzy logic to social choice theory, CRC Press, 2015.

H. T. Nguyen and M. Sugeno, Fuzzy systems: modeling and control, vol. 2, Springer Science & Business Media, 1998.

J. R. Ni no Quevedo, Ecuaciones diferenciales difusas: Una forma de modelar la incertidumbre y la ambig¨uedad., 2015.

W. Pedrycz and F. Gomide, Fuzzy systems engineering: toward humancentric computing, John Wiley & Sons, 2007.

T. J. Ross, Fuzzy logic with engineering applications, John Wiley & Sons, 2009.

M. Spivak, C´alculo infinitesimal, Revert´e, 1996.

L. H. Tsoukalas and R. E. Uhrig, Fuzzy and neural approaches in engineering, John Wiley & Sons, Inc., 1996.

M. J. Wierman, An introduction to the mathematics of uncertainty, (2010).

L. A. Zadeh, Fuzzy sets, Information and control 8 (1965), no. 3, 338–353.

, The concept of a linguistic variable and its application to approximate reasoning - i, Information sciences 8 (1975), no. 3, 199–249.

, The concept of a linguistic variable and its application to approximate reasoning - ii, Information sciences 8 (1975), no. 4, 301–357.

, The concept of a linguistic variable and its application to approximate reasoning-iii, Information sciences 9 (1975), no. 1, 43–80.

, Fuzzy sets, fuzzy logic, and fuzzy systems: selected papers, 1996.

H. Zarei, A. Kamyad, and A. A. Heydari, Fuzzy modeling and control of hiv infection, Computational and mathematical methods in medicine 2012 (2012).

H. Zhang and D. Liu, Fuzzy modeling and fuzzy control, Springer Science & Business Media, 2006.

H. J. Zimmermann, Fuzzy sets, decision making, and expert systems, vol. 10, Springer Science & Business Media, 1987.

, Fuzzy set theory and its applications, Springer Science & Business Media, 2001.

Visitas a la página del resumen del artículo

637

Descargas

Los datos de descarga aún no están disponibles.

Cómo citar

Niño Quevedo, J. R. (2017). Conjuntos difusos. Una forma de representar la imprecisión y la subjetividad. Boletín De Matemáticas, 24(1), 57-89. https://revistas.unal.edu.co/index.php/bolma/article/view/66863

Licencia

Derechos de autor 2017 Boletín de Matemáticas

Creative Commons License

Esta obra está bajo una licencia internacional Creative Commons Atribución 4.0.